A193643 - OEIS

A193643

Number of arrays of -3..3 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero

1, 7, 19, 67, 217, 721, 2377, 7855, 25939, 85675, 282961, 934561, 3086641, 10194487, 33670099, 111204787, 367284457, 1213058161, 4006458937, 13232434975, 43703763859, 144343726555, 476734943521, 1574548557121, 5200380614881

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OFFSET

1,2

COMMENTS

Column 3 of A193648

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +a(n-3).

Empirical: G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x^2+3*x-1) ). - R. J. Mathar, Feb 19 2015

Empirical: a(n)+a(n+1) = 2*A003688(n+1). - R. J. Mathar, Feb 19 2015

EXAMPLE

Some solutions for n=6

..2....1...-1....0....0....0....1....0....2...-2....2....1...-3....0....0....0

.-2...-1....1...-1...-3....0...-1....3...-2....2...-2...-1....3...-2....0....0

.-1....1....2....1....3....0....1...-3....2...-3...-2...-3....1....2....2....0

..1....0...-2...-3...-1...-2....1....3....0....3....2....3...-1....0...-2...-3

.-1...-3....0....3....1....2...-1...-3...-2....0....1...-2....2....2....2....3

..0....3....0...-3....0....0....1....0....2....0...-1....2...-2...-2...-2....0

CROSSREFS

Sequence in context: A155218 A305483 A046137 * A228026 A122484 A155242

Adjacent sequences: A193640 A193641 A193642 * A193644 A193645 A193646

KEYWORD

nonn

AUTHOR

R. H. Hardin Aug 02 2011

STATUS

approved